Abstract
In this paper, we classify the fixed point data (weights and signs at the fixed points), of a circle action on a 6-dimensional compact connected oriented manifold with 4 fixed points. We prove that it agrees with that of an equivariant connected sum along free orbits of rotations on two 6-spheres, or that of a linear action on \({{\mathbb {C}}}{\mathbb {P}}^3\). The former case includes that of Petrie’s exotic action on \({\mathbb {C}}{\mathbb {P}}^3\).
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Donghoon Jang was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (2021R1C1C1004158).
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Jang, D. Circle actions on 6-dimensional oriented manifolds with 4 fixed points. J. Fixed Point Theory Appl. 25, 68 (2023). https://doi.org/10.1007/s11784-023-01070-y
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DOI: https://doi.org/10.1007/s11784-023-01070-y